is called hypermomentum [1]} and encodes the microscopic characteristics of matter such as spin, dilation and shear. In the same way that the energy momentum tensor sources spacetime curvature by means of the metric field equations, the hypermomentum is the source of spacetime torsion and non-metricity (through the connection field equations). Note that these energy related tensors are not quite independent and are subject to the conservation law
\(\sqrt{-g}(2 \tilde{\nabla }_{\mu }T^{\mu }_{\;\;\alpha }-\Delta ^{\lambda \mu \nu }R_{\lambda \mu \nu \alpha })+\hat{\nabla }_{\mu }\hat{\nabla }_{\nu }(\sqrt{-g}\Delta _{\alpha }^{\;\;\mu \nu })+2S_{\mu \alpha }^{\;\;\;\;\lambda }\hat{\nabla }_{\nu }(\sqrt{-g}\Delta _{\lambda }^{\;\;\;\mu \nu })=0\;, \;\; \hat{\nabla }_{\mu }:=2S_{\mu }-\nabla _{\mu } \) 
